## anonymous 4 years ago limit of (5x+2)/sqrt(9x^2+3x+1)-x as x approaches -infinity

1. anonymous

$\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+3 x+1}-x},x\to \text{Infinity}\right]=\frac{5}{2}$

2. anonymous

rob its approaching negative infinity

3. anonymous

also can you please demonstrate in steps. i need to understand how to to dow this. and the denominator is actually sqrt(9x^2+x-3) sorry

4. anonymous

crap let me rewrite the question... i made alot of mistakes

5. anonymous

$\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}$

6. anonymous

Sorry. missed the -infinity requirement.$\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+ x-3}},x\to -\text{Infinity}\right]=-\frac{5}{3}=1.6667$A plot of the problem expression from -100 throught zero is attached. Cannot help you on the solution process. Using Mathematica for the answers and plot generation.

7. anonymous

ok this is the last one, do you think you can help me $\lim_{x \rightarrow infinity}\sqrt{x^2+3x+1}-x$

8. anonymous

I'll try

9. anonymous

$\text{Limit}\left[\sqrt{x^2+3 x+1}-x,x\to \text{Infinity}\right]=\frac{3}{2}=1.5$Refer to the attached plot.